There are primary uses of statistical graphics for reporting our data.
As a report or summary of the “raw” data.
As a visualization of the results of a statistical model, supplementing a model summary table.
Supplementing a table of coefficients.
Contextualizing the results.
As the only viable report of the model.
When there are too many parameters, or they’re too uninterpretable for any other kind of report. (e.g. gams)
Graphs Matter
For many readers (and the field), what is communicated in graphs will endure in their memory and understading of your work longer than what is written in the text.
Pitfalls and Open Questions
Pitfalls
There is often insufficient detail in the description of figures to sufficiently understand what is being plotted.
Care must be taken in making inferences based on figures.
Open Questions
How “raw” should the raw data in a summary plot be?
What is the appropriate trade-off between visual legibility and rigor?
It overstates how much data you have. There might be 19,000 tokens, but there are only 326 speakers.
The smoothers chase trends that are really individual-based.
The smoothers underestimate the uncertainty.
Summarized Data
Pros
It more accurately captures the quantity of data you’re doing inference over.
The smoothers are less distracted by individual speakers w/ lots of data.
Cons
You lose a sense of the total volume of data.
You lose a sense of the variance of over-all production.
Recommendation:
Figure XX: A plot of normalized F1 over speakers’ year of birth. Each point represents the average normalized F1 for each speaker for each following place of articulation, with penalized cubic regression splines overlaid.
Recommendation:
When the raw data points inhibit legibility too much.
Figure XX: Estimated normalized F1 over speakers’ year of birth. Penalized cubic regression splines fit over speaker-level averages.
Averaging Methods
Averaging Methods
It’s crucially important to describe how averages were estimated. You could lump all the data together:
Averaging Methods
Or, you could average within speakers first, then within place.
Averaging Methods
Or, you could average within words within speakers, then within speakers, then within place.
When possible, estimate means based on the nested structure of the data, and say so.
Averages were estimated by first estimating word-level averages within speakers, then speaker level averages within place of articulation, then global averages for place of articulation.
Figures display incremental averages with words nested within speakers nested within place of articulation.
Model Visualization
Model Visualization
Sometimes, it is advisable to visualize the output of a statistical model.
A visual display can sometimes more clearly communicate the effects.
A visual display can sometimes show non-obvious relationships.
Figure XX. Estimated difference curve between /ayk/ and /ayt/